Wyatt Earp Rides Again - S6-E20
Continuity mistake: After Opie tells Andy that he knows he'll win at high noon, it cuts to Warren in front of Floyd's shop (with its furniture conspicuously missing), but later when Andy walks over to Floyd's shop its facade has changed. Note differences such as window structure, and the name "Floyd's Barber Shop" painted on the window which wasn't in the earlier shot. (00:18:05 - 00:24:15)
Answer: It was a joke. They were supposed to be dumb hillbillies.
Both. According to later interviews with both Andy and the Dillards band (the real name of the band that played the parts of the Darling children, of which Charlene (Maggie Peterson - Mancuso was also a member) the reason the Darling boys never had any lines was because they would've had to have been paid if they spoke. In return for appearing without lines or pay, Andy promised to get as much of their music onto the show as possible which, he did. This obviously gave them a lot of exposure.